Maximal and minimal solutions of an Aronsson equation: $L^{\infty }$ variational problems versus the game theory

Yifeng Yu

The Dirichlet problem $$ \begin{cases} Δ_{\infty}u-|Du|^2=0 \quad \text{on $Ω\subset \Rset ^n$} u|_{\partial Ω}=g \end{cases} $$ might have many solutions, where $Δ_{\infty}u=\sum_…